In the state of the art, various methods are known for three-dimensionally reconstructing a specular surface of an article, as shown in the prior art such as “Transparent and specular object reconstruction” published in Computer Graphics Forum 2010 by Ivo Ihrke, Kiriakos N. Kutulakos, Hendrik P. A. Lensch, Marcus Magnor, and Wolfgang Heidrich.
By way of example, the article entitled “Shape from distortion: range scanning of mirroring objects” published in Siggraph 2002: Conference abstracts and applications (2002) by M. Tarini, H. P. A. Lensch, M. Goesele, and H. P. Seidel, edited by D. Roble, describes a method of three-dimensionally reconstructing specular surfaces based on the principle of observing the reflection of a known light pattern. That technique assumes surface continuity and proceeds by integration to work back to the shape of the article. That method is complex in terms of calculation, and it operates correctly only with a high density of measurement points, over surfaces without any major discontinuity and after setting correct initial values for starting the integration. That method, which requires complex calculations, is found to be difficult to perform in an industrial setting. Furthermore, that technique is not suitable for measuring a plurality of superposed surfaces in transparent media.
The article entitled “Shape from polarization: a method for solving zenithal angle ambiguity” (Christophe Stolz, Mathias Ferraton, Fabric Mériaudeau, Optics Letters 37, 20 (2012) 4218 describes a method of three-dimensionally reconstructing surfaces using an extended diffuse light source and information about the polarization of light reflected on the article. The orientations of normals to the external specular surface of an article are deduced from the polarization. That method thus requires an integration step in order to work back to the three-dimensional surfaces. That method operates correctly only with a high density of measurement points on surfaces without major discontinuity and by having correct initial values at the beginning of the integration. That method, which requires complex calculations, is found to be difficult to perform in an industrial setting. Furthermore, that technique is not suitable for measuring a plurality of superposed surfaces in transparent media.
In analogous manner, Documents U.S. Pat. No. 5,028,138 and US 2010/290713, and the publication by G. A. Atkinson et al. “Recovery of surface orientation from diffuse polarization” describe methods of reconstructing articles from polarization parameters. Nevertheless, the methods described in those documents present the same drawbacks as the technique described in the publication “Shape from polarization . . . ”.